
'''simple docstring'''






def 		A_							(						_lowerCAmelCase :     list[list]				):



      """simple docstring"""




      _lowerCamelCase					: List[str]		    = current_set.copy()
      for row_index, row in enumerate(_lowerCAmelCase				):
            _lowerCamelCase					: Optional[int]		    = row[0]
            for column_index, column in enumerate(_lowerCAmelCase				):
                  if magnitude == 0:
                        _lowerCamelCase					: Optional[Any]		    = column
                        continue
                  _lowerCamelCase					: List[str]		    = column / magnitude
    # Subtract to cancel term
      _lowerCamelCase					: List[str]		    = current_set[0]
      _lowerCamelCase					: Dict		    = [first_row]
      _lowerCamelCase					: Union[str, Any]		    = current_set[1::]
      for row in current_set:
            _lowerCamelCase					: int		    = []
            # If first term is 0, it is already in form we want, so we preserve it
            if row[0] == 0:
                  final_set.append(_lowerCAmelCase				)
                  continue
            for column_index in range(len(_lowerCAmelCase				)				):
                  temp_row.append(first_row[column_index] - row[column_index]				)
            final_set.append(_lowerCAmelCase				)
      # Create next recursion iteration set
      if len(final_set[0]				) != 3:
            _lowerCamelCase					: Optional[Any]		    = final_set[0]
            _lowerCamelCase					: List[str]		    = []
            _lowerCamelCase					: Optional[Any]		    = []
            for row in final_set[1::]:
                  current_first_column.append(row[0]				)
                  next_iteration.append(row[1::]				)
            _lowerCamelCase					: Optional[int]		    = simplify(_lowerCAmelCase				)
            for i in range(len(_lowerCAmelCase				)				):
                  resultant[i].insert(0					,						current_first_column[i]				)
            resultant.insert(0					,						_lowerCAmelCase				)
            _lowerCamelCase					: Any		    = resultant
      return final_set







def 		A_							(						_lowerCAmelCase :     list[list]				):



      """simple docstring"""




      if len(_lowerCAmelCase				) == 0:
            raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
      _lowerCamelCase					: str		    = len(_lowerCAmelCase				) + 1
      if any(len(_lowerCAmelCase				) != _length for item in equations				):
            raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
      for row in equations:
            if any(not isinstance(_lowerCAmelCase					,						(int, float)				) for column in row				):
                  raise ValueError("solve_simultaneous() requires lists of integers"				)
      if len(_lowerCAmelCase				) == 1:
            return [equations[0][-1] / equations[0][0]]
      _lowerCamelCase					: int		    = equations.copy()
      if any(0 in row for row in data_set				):
            _lowerCamelCase					: Union[str, Any]		    = data_set.copy()
            _lowerCamelCase					: Optional[Any]		    = []
            for row_index, row in enumerate(_lowerCAmelCase				):
                  if 0 not in row:
                        _lowerCamelCase					: Dict		    = data_set.pop(_lowerCAmelCase				)
                        break
            if not full_row:
                  raise ValueError("solve_simultaneous() requires at least 1 full equation"				)
            data_set.insert(0					,						_lowerCAmelCase				)
      _lowerCamelCase					: Union[str, Any]		    = data_set.copy()
      _lowerCamelCase					: Union[str, Any]		    = simplify(_lowerCAmelCase				)
      _lowerCamelCase					: int		    = simplified[::-1]
      _lowerCamelCase					: list		    = []
      for row in simplified:
            _lowerCamelCase					: List[Any]		    = row[-1]
            if not solutions:
                  if row[-2] == 0:
                        solutions.append(0				)
                        continue
                  solutions.append(current_solution / row[-2]				)
                  continue
            _lowerCamelCase					: Optional[int]		    = row.copy()[: len(_lowerCAmelCase				) - 1 :]
            while temp_row[0] == 0:
                  temp_row.pop(0				)
            if len(_lowerCAmelCase				) == 0:
                  solutions.append(0				)
                  continue
            _lowerCamelCase					: List[str]		    = temp_row[1::]
            _lowerCamelCase					: Union[str, Any]		    = temp_row[::-1]
            for column_index, column in enumerate(_lowerCAmelCase				):
                  current_solution -= column * solutions[column_index]
            solutions.append(_lowerCAmelCase				)
      _lowerCamelCase					: Tuple		    = []
      for item in solutions:
            final.append(float(round(_lowerCAmelCase					,						5				)				)				)
      return final[::-1]


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 UpperCAmelCase_							: Union[str, Any] =							[
     [2, 1, 1, 1, 1, 4],
     [1, 2, 1, 1, 1, 5],
     [1, 1, 2, 1, 1, 6],
     [1, 1, 1, 2, 1, 7],
     [1, 1, 1, 1, 2, 8],
 ]
 print(solve_simultaneous(eq))
 print(solve_simultaneous([[4, 2]]))





'''simple docstring'''


import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment





@require_huggingface_suite
class  __lowercase    (	unittest.TestCase			):







   def 		UpperCamelCase__      (						self   )					->     Tuple:
     __a								=       inspect.getfile(accelerate.test_utils   )
     __a								=       os.path.sep.join(
         mod_file.split(os.path.sep   )[:-1] + ['scripts', 'external_deps', 'test_metrics.py']   )

     from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

     __a								=       test_metrics







   @require_cpu
   def 		UpperCamelCase__      (						self   )					->     Tuple:
     debug_launcher(self.test_metrics.main   ,				num_processes=1   )







   @require_cpu
   def 		UpperCamelCase__      (						self   )					->     str:
     debug_launcher(self.test_metrics.main   )







   @require_single_gpu
   def 		UpperCamelCase__      (						self   )					->     Dict:
     self.test_metrics.main()







   @require_multi_gpu
   def 		UpperCamelCase__      (						self   )					->     int:
     print(f"Found {torch.cuda.device_count()} devices."   )
     __a								=       ['torchrun', f"--nproc_per_node={torch.cuda.device_count()}", self.test_file_path]
     with patch_environment(omp_num_threads=1   ):
       execute_subprocess_async(UpperCamelCase   ,				env=os.environ.copy()   )



